The Mechanism · Gated-generation receipt

gen-define-depth-first-versus-breadth-first-search-and-give-one-5a1d

stable pending witness
2026-05-29 05:51:57 UTC · anthropic/claude-sonnet-4-5

Prompt

Define depth-first versus breadth-first search and give one short worked example.
81 chars

Generation

# Depth-First Search (DFS) vs Breadth-First Search (BFS) ## Definitions **Depth-First Search (DFS)**: Explores as far down one branch as possible before backtracking. Uses a **stack** (or recursion). **Breadth-First Search (BFS)**: Explores all neighbors at the current level before moving deeper. Uses a **queue**. ## Worked Example Search for node **5** in this tree: ``` 1 / \ 2 3 / \ 4 5 ``` ### DFS (left-to-right): - Visit: **1** → 2 → 4 (dead end, backtrack) → **5** ✓ Found! - Path: 1 → 2 → 4 → 2 → 5 ### BFS (level-by-level): - Level 0: Visit **1** - Level 1: Visit **2**, **3** - Level 2: Visit **4**, **5** ✓ Found! - Path: 1 → 2 → 3 → 4 → 5 ## Key Difference - **DFS** goes deep first (1→2→4→5) - **BFS** goes wide first (1→2,3→4,5)
24 tokens in · 318 tokens out · 6410 ms · $0.0048

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
6419.3 ms
Base LLM
6410.1 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0048

Trail

05:51:57 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
05:51:57 red_gate decision=pass reason=no disqualifying input patterns detected
05:52:04 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=318 latency_ms=6410.1 cost_usd=0.0048
05:52:04 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:52:04 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:52:04 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:52:04 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:52:04 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:52:04 signed hash_algo=sha256 hash=sha256:9434c478ea33f4ca284d809490f6e55acc6832a1fe93b93fdd0d2cd409fcb79e

Content hash

sha256:9434c478ea33f4ca284d809490f6e55acc6832a1fe93b93fdd0d2cd409fcb79e

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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